Towards using direct methods in seismic tomography: Computation of the full resolution matrix using high-performance computing and sparse QR factorization

Abstract

For more than two decades, the number of data and model parameters in seismic tomography problems has exceeded the available computational resources required for application of direct computational methods, leaving iterative solvers the only option. One disadvantage of the iterative techniques is that the inverse of the matrix that defines the system is not explicitly formed, and as a consequence, the model resolution and covariance matrices cannot be computed. Despite the significant effort in finding computationally affordable approximations of these matrices, challenges remain, and methods such as the checkerboard resolution tests continue to be used. Based upon recent developments in sparse algorithms and highperformance computing resources, we show that direct methods are becoming feasible for large seismic tomography problems. We demonstrate the application of QR factorization in solving the regional P-wave structure and computing the full resolution matrix with 267 520 model parameters.